Decision tree: more than 2 classes, how to represent elements that are in a class vs ones that aren't?
I don't think that is possible with a decision tree, unless there is some measure of confidence that you can use as a threshold.

I ran into the same problem with the ID3 algorithm. It assigns classes, but you only have the resulting class without any confidence or probability attached.

One possible solution could be to add a number of counter examples as a second (dummy, catch-all) class; if the elements of C = 0 are reasonably tightly clustered and your counter examples for C != 0 cover the remaining problem space, then that might work.